This PDF book covers the following
topics related to Fractals in Probability and Analysis : Minkowski and Hausdorff
dimensions, Self-similarity and packing dimension, Frostman’s theory and
capacity, Self-affine sets, Graphs of continuous functions, Brownian motion,
Random walks, Markov chains and capacity, Besicovitch–Kakeya sets, The Traveling
Salesman Theorem.
Author(s): Christopher J. Bishop Stony Brook
University, Yuval Peres Microsoft Research
This PDF book covers the following
topics related to Fractals in Probability and Analysis : Minkowski and Hausdorff
dimensions, Self-similarity and packing dimension, Frostman’s theory and
capacity, Self-affine sets, Graphs of continuous functions, Brownian motion,
Random walks, Markov chains and capacity, Besicovitch–Kakeya sets, The Traveling
Salesman Theorem.
Author(s): Christopher J. Bishop Stony Brook
University, Yuval Peres Microsoft Research
This book is devoted to a phenomenon of
fractal sets, or simply fractals. Topics covered includes: Sierpinski gasket,
Harmonic functions on Sierpinski gasket, Applications of generalized numerical
systems, Apollonian Gasket, Arithmetic properties of Apollonian gaskets,
Geometric and group-theoretic approach.
This note covers the following topics: Thomasina's Geometry of
Irregular Forms, The Chaos Game, The Sierpinski Hexagon, Thomasina's Fern
and Valentine's Grouse.